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Solutions Manual x Fluid Mechanics, Fifth Edition
z1 z2 ! 0 by definition. Therefore, flow is down. Ans.
Thus h f
While flowing down, the pressure drop due to friction exactly balances the pressure rise
due to gravity. Assuming laminar flow and noting that 'z L, the pipe length, we get
128P LQ
SUgd 4
hf
or: Q
S (8.70)(9.81)(0.025)4
128(0.104)
'z
L,
7.87E4
m3
s
2.83
m3
h
Ans.
6.24 Two tanks of water at 20qC are connected by a capillary tube 4 mm in diameter
and 3.5 m long. The surface of tank 1 is 30 cm higher than the surface of tank 2.
(a) Estimate the flow rate in m3/h. Is the flow laminar? (b) For what tube diameter will
Red be 500?
Solution: For water, take U 998 kg/m3 and P 0.001 kg/m˜s. (a) Both tank surfaces
are at atmospheric pressure and have negligible velocity. The energy equation, when
neglecting minor losses, reduces to:
'z
0.3 m
128P LQ
SUgd 4
hf
Solve for Q
4UQ/(SPd) and 'z
Re d
hf
0.3 m
m3
0.019
h
Ans. (a)
4(998)(5.3E6)/[S (0.001)(0.004)]
1675 laminar. Ans. (a)
Re d
500
m3
5.3E6
s
4 UQ/(SP d )
Check Re d
(b) If Red
128(0.001 kg/m˜s)(3.5 m)Q
S (998 kg/m3 )(9.81 m/s2 )(0.004 m)4
500
hf, we can solve for both Q and d:
4(998 kg/m3 )Q
, or Q
S (0.001 kg/m˜s)d
0.000394d
128(0.001 kg/m˜s)(3.5 m)Q
, or Q
S (998 kg/m3 )(9.81 m/s2 )d 4
Combine these two to solve for Q 1.05E6 m 3 /s and
d
20600d 4
2.67 mm
Ans. (b)